Some aspects about the lattice [τg,χ] and the torsion theories of Kaplansky-type

Abstract

In this manuscript, we define when a torsion theory, which is a generalization of Goldie’s torsion theory, is of the type I, II, or III, according to Kaplansky’s theory of types, and we establish some structure theorems of regular, right self-injective rings using the torsion theories of Kaplansky-type. We study the properties that each of these torsion theories has and their influence on the lattice of generalizations of Goldie’s torsion theory, locating several subintervals of which contain no atoms nor coatoms, thus extending our knowledge of the lattice structure of .